Approximate pi to 24 digits via keyboard

[Dieter]

(02-06-2015 04:10 PM)PANAMATIK Wrote:  I verified HP-67/97 HP34C HP29C, they compute the same values as above.

That's what could be expected for calculators of that era.

(02-06-2015 04:10 PM)PANAMATIK Wrote:  But HP-21 HP-25/HP-25C both produce the same even less accurate values, interestingly with more decimals. Obviously they use a different algorithm.

The algorithms may even be similar, but the internal precision is not. Starting with the HP91, 67 and 97 in 1976 HP used 13 internal digits for most calculations to minimize roundoff errors. This was not yet available on earlier calculators like the 21 and 25 that appeared in 1975.

This is what HP Journal 1976-11 says on page 17 ("The New Acccuracy: Making 2³ = 8" by Dennis W. Harms):

Quote:The second method of improving accuracy is to trap critical arguments and calculate the functions at these arguments in a special way. These critical arguments include numbers near 1 when calculating ln or log, numbers near 0 when calculating sin^-1, cos^-1, or tan^-1, and numbers near zero or multiples of π/2 when calculating sin, cos, or tan.

(Emphasis added)

So indeed some algorithms have been updated in the "new accuracy calculators".

Dieter